Draw a directed graph for the relation R on the set {0, 1, 2, 3) given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.
Draw a directed graph for the relation R on the set {0, 1, 2, 3) given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
Draw a directed graph for the relation \( R \) on the set \(\{0, 1, 2, 3\}\) given by:
\[ R = \{ (0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3) \} \]
**Explanation:**
The directed graph (or digraph) of a relation involves creating vertices for each element in the set and drawing directed edges (arrows) according to the ordered pairs in the relation.
**Vertices:**
- The set of vertices is \{0, 1, 2, 3\}.
**Edges:**
- There is a directed edge from 0 to 1, since \((0, 1) \in R\).
- There is a directed edge from 0 to 2, since \((0, 2) \in R\).
- There is a directed edge from 1 to 2, since \((1, 2) \in R\).
- There is a loop at 2, since \((2, 2) \in R\).
- There is a directed edge from 3 to 1, since \((3, 1) \in R\).
- There is a loop at 3, since \((3, 3) \in R\).
**Graph Characteristics:**
- Each vertex corresponds to an element in the set \{0, 1, 2, 3\}.
- The edges are directed, indicating the relationship direction between elements.
- Loops at a vertex indicate a relation from an element to itself.
Visualizing this will help understand how these elements are related to each other within the set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba0f63d0-54c5-484b-bd26-dd830c37503b%2F5ea36481-c1e0-4ad3-b569-9cd02e8b3ff1%2F1yguguo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Draw a directed graph for the relation \( R \) on the set \(\{0, 1, 2, 3\}\) given by:
\[ R = \{ (0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3) \} \]
**Explanation:**
The directed graph (or digraph) of a relation involves creating vertices for each element in the set and drawing directed edges (arrows) according to the ordered pairs in the relation.
**Vertices:**
- The set of vertices is \{0, 1, 2, 3\}.
**Edges:**
- There is a directed edge from 0 to 1, since \((0, 1) \in R\).
- There is a directed edge from 0 to 2, since \((0, 2) \in R\).
- There is a directed edge from 1 to 2, since \((1, 2) \in R\).
- There is a loop at 2, since \((2, 2) \in R\).
- There is a directed edge from 3 to 1, since \((3, 1) \in R\).
- There is a loop at 3, since \((3, 3) \in R\).
**Graph Characteristics:**
- Each vertex corresponds to an element in the set \{0, 1, 2, 3\}.
- The edges are directed, indicating the relationship direction between elements.
- Loops at a vertex indicate a relation from an element to itself.
Visualizing this will help understand how these elements are related to each other within the set.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
